Discussion regarding the art and science of creating holes of low entropy, shifting them around, and then filling them back up to operate some widget.

30 April 2006

Proclivity of Wind Power

So the question has been asked on my blog and elsewhere: we know wind is intermittent, but what does that mean exactly? I thought a simple case study might help illuminate some of the issues involved. HOMER is the obvious choice in software to simulate this without a lot of programming.

System Specifications

I decided to design a system with a constant demand of 26 MW. That power can be supplied either by 100 WES30 (a Dutch manufacturer) wind turbines (each rated at 260 kW) or a 26 MW monolithic gas turbine with a peak efficiency of 46.0 %. However, the efficiency of the system declines at lower loads [Figure 1].

Figure 1: Efficiency versus load for gas turbine.

Typically we would expect a capacity factor of about 20 % for wind turbines. This correlates to a 20 % penetration of the energy supply by wind in my example, a commonly held 'threshold' for where we expect to see significant problems emerge.

Figure 2: Turbine power output versus wind speed. Cuts out at about 4 m/s and feathers at 260 kW and 18 m/s.

Turbine output is similarly variable with wind speed [Figure 2]. Notice that the wind turbine with the 300 kW rating maxes out at 260 kW. The hourly wind data is for Block Island, RI, USA (I would have preferred Cape Cod but I don't have any) with an average windspeed of 4.83 m/s.

In addition to the experimental case, I also designed a reference which was 100 % gas in order to compare the CO2 emissions and cost.

Results

The wind turbines ended up meeting 21 % of the total demand with an average power output of 5.467 MW. Of course, the

Figure 3: Hourly turbine output for two weeks in March (click to see larger image).

The gas turbine burned $15,900,000 worth of natural gas over the year (at $10.00/mcf) . It produced a total of 86,270,000 kg of CO2 over the year. So how does this compare to the reference case? Considering that wind provided 21 % of the power, we might assume that the mixed system would burn 79 % of the gas and produce a similar proportion of the greenhouse gas emissions. However, as one can observe from [Figure 1], as the wind power increases the efficiency of the gas turbine is reduced. In actuality, the reference system burned $17,790,00 worth of natural gas and produced 96,650,000 tons of CO2. Thus, while wind produces 21 % of the power in the mixed set-up it only mitigates 11 % of the fuel cost and greenhouse gas emissions.

Figure 4: False-colour graph of wind power output as a function of time and date.

As we can see from [Figure 4] there is significant variation in the wind output both hour to hour and seasonally. Note the large black spots in the summer months; long periods of low power production are obviously a huge drawback if you are trying to use some sort of storage system like batteries. It implies you need a great big buffer. Alternatively, if you are trying to do load following with a gas turbine, you can't rely on any of the wind power being steady. In fact, you have to maintain the same power plant capacity with wind as you do without. All of the capital investment in wind needs to be offset through lower fuel consumption of fossil resources.

Sources of Error

There are a number of issues I am glossing over here which favour either side of the argument. For wind power, I am calculating the power output for a single set of wind data. If turbines are geographically separated, they gain the advantage of sample averaging. The wind will tend to blow more steadily if averaged over a larger area.

Against wind power, I am modeling demand as constant. This is quite wrong -- in fact the hourly and seasonal variations in electricity demand are quite substantial. This means that not only does the load-following gas turbine have to coup with the volatility of wind but also that of the consumer. One point of interest is that the gas turbine runs continuously -- it never has to stop -- which isn't realistic either.

Also, one should consider that the location of the wind turbine is quite important. Studies from the UK and Germany have come to widely diverging conclusions on the utility of wind. This is largely due to the differences in geography. The wind tends to blow more steadily in some areas. While companies may be picking their wind farm locations based on mean wind speed perhaps they should be just as concerned with the higher order statistical moments (variance, skewness, and kurtosis).

18 comments:

Anonymous
said...

Very interesting. This is the first time I’ve seen anyone attempt this. Wind speed data from sites closer to Cape Cod can be found at the Martha’s Vineyard Coastal Observatory site-http://mvcodata.whoi.edu/cgi-bin/mvco/mvco.cgiOr from the NOAA National Data Buoy Center- Buzzard’s Bay Stationhttp://www.ndbc.noaa.gov/station_page.php?station=buzm3

The other source of error is that a real system will have more than one gas turbine, and superfluous turbines are likely to be turned off rather than run at idle.

This is an argument for real-time DSM, because a grid which can manage its load to exactly consume the output of un-schedulable production like wind will be able to minimize the low-power operation of gas turbines and other peaking generators.

You're taking too much from a simplistic analysis. The graph I gave only lists the instantaneous efficiency of the system, as if it's been running at that load since the beginning of the universe. As we all know, introducing transients doesn't make a heat engine happy.

If you have to constantly turn on and off sets of gas turbines that will have a great negative impact on their performance. You need to give them enough heat and inertia to get to their operating conditions. That's all wasted energy that Homer can't really account for. The wind data is only hourly. In reality wind oscillates much more frequently – corrections on the order of a minute are necessary.

There is a more detailed (and public domain) Irish study that can give a better feel for this:

46% is rather low for a combined-cycle plant (a 30 MW GE simple-cycle gas turbine gets over 38%), so I had assumed that you were considering a peaking plant rather than base-load.

Wind fluctuates on a scale of minutes, but DSM systems which can make up the difference by juggling between A/C compressors and stored ice, water at the top of a water heater vs. the bulk of the tank, and (later) chargers for electric vehicles could manage this easily. If you have even 20 million PHEV's on 110 volt 15 A connections, you've got 33 GW of demand which is potentially controllable. That's only about 3.5% of total US generating capacity, but as a fraction of the minute-by-minute variation in supply I'm sure it's far more than that. Put them on 220 V 30 A connections or expand the total well past 10% of the vehicle fleet, and you're talking some serious impact.

Wow! According to the Irish study, "The additional cost of operating reserve is relatively small and likely to be to less than €0.50/MWh with 1950MW."

That's only .05 cents per KWHr! and that's with wind at a decent market share of about 12% (assuming 30% capacity factor, and Ireland's average generation at 4.82 GW).

Keep in mind that Ireland is pretty small (smaller than the US state of Maine), and there's very little interconnection with Britain (about 6% of generation), so Ireland would get relatively little benefit of geographical dispersion and averaging. This is common in Europe, but not in the US (with the hopefully temporary exception of Texas).

That seems to be a pretty strong statement that wind's variability is not that hard to deal with.

I wouldn't take that as gospel. You point on lack of geographical separation is moot. The correlation among wind speed at different farms in their modeling methodology is handled in an arbitrary fashion (see B.19). What's promising about the Ilex study is that it suggests that if you have strong forecasting techniques you can reduce the problems. Thus far wind forecasting is more voodoo than science.

Here is the 'other' Irish study from the power company (these are generally taken as a pair but I couldn't find this one last night):

This is actually the better study because they are the utility and have proprietary data. They have much more negative conclusions: 15 % cost increase in the price of electricity for only 11.7 % wind penetration and €120/ton cost for CO2 reduction. In comparison the Ilex study is quoting €0.50/ton. Those two numbers are difficult to reconcile. The Ilex number's don't account for capital costs (wheras the ESB study does estimate them).

That's nice, and I generally agree, but plug-ins and thermal storage are vapourware at this point. Similarly pumped/reservoir hydro can provide buffering from the supply side (and those systems actually exist).

I know that some of my former professors at UVic are working on the synergy between hydro and intermittent wind and wave power but I haven't seen publications as of yet.

Firstly, the assumption that adding wind power stops gas turbines working at maximum capacity is false, since generator capacity will be sized for peak demand, not average.

Secondly, all energy generators, including gas turbines, have downtime for maintenance etc, seehttp://www.bwea.com/energy/rely.html for some numbers. So the nominal total capacity has to be greater than expected peak demand anyway.

The way to reduce the variability in supply (and hence the required overcapacity and the inefficient stop/start of baseload generators) is to diversify the energy sources, so adding wind power will actually improve the net efficiency of gas turbines in the system.

I haven't had time to really take the ESB study apart, but I note that the average cost per kwhr of the reference 6.5 GW NG system seems to be about $.033. This would seem to be badly out of date (the study compilation date looks like late 2003, when Irish NG prices were probably less than a third what they are currently). The marginal cost of wind appears to come out to about $.076 per kwhr, which is almost certainly less than the current cost of electricity from Irish NG.

Again, this is a very small system - we're talking about a 6.5 GW (peak)system, compared to 905 GW in the US. Ireland is very small, and only barely interconnected to the UK. $.076 per kwhr in such an environment doesn't seem too bad - less than NG, less than coal (fully loaded with external costs and overhead).

It would be interesting to see a comparison with nuclear in such a small system. In the US you can have 10 1 GW nuclear plants, each of which is out of operation 10% of the time for refueling, and get a continuous 9 GW. In this system you couldn't justify more than about 1.5GW of nuclear, (the night time base load), and the one or two nuclear plants would require 100% backup capacity during refueling, not to mention the week it takes to re-start a nuclear plant after a power outage.

1.) Hypothesis of a false state implies nothing. Wind provides statistically insignificant firm capacity. The standard deviation has always extended down into the bogus negative realm in my experience, and that's only a 68 % confidence interval. For the data set in my example the mean power output was 28.5 MW +/- 43.85 MW. If you don't believe me, run your own numbers.

Robert, if I understand you correctly, you seem to be saying that wind has a very large output variance, so large that wind can provide no contribution to capacity factor. Do you have any references for that? Everything I've seen says that it does. The AWEA says that it does for low market share (e.g., that wind generation with 30% capacity factor provides a 30% contribution to system capacity up to say, 10% market share), and that the contribution slowly diminishes above that point.

I think you may be missing Toby's point. All generation has variance in output, not just wind. Nothing is 100% reliable - everything is a statistical question. To dismiss wind as unreliable is not realistic.

Clearly wind's variation is greater, but how much greater is not clear. That’s what I was trying to get at in my discussion of nuclear, above. If you work with a very small system, any generator is going to need 100% backup. As you scale up, the ratio of variance to average load gets smaller - that’s a basic statistical principle, and it applies here very strongly. This means that analysis of small simulations, or small systems, tells you very little about the behavior of large systems: the relationship of variance (or, more properly, variance divided by the mean) to system size is non-linear. To phrase it in yet another way, the % of system capacity needed to meet peak loads drops as the system gets larger. That means that a small wind system that would need 100% backup as a standalone system may only need 10% backup when added to a system that is 10 times larger.

Here’s an example: E.ON Netz in their report at "http://www.eon-energie.de/bestellsystem/ frameset_eng.php?choosenBu=eonenergie&choosenId=1725" shows some capacity contribution, about 9%, which is 50% of their 18% capacity factor.

And, again, that’s for a very small system. E.ON Netz is the TSO for two of Germany's 16 states, with an area of 22,822 square miles. This is very small, about the size of W. Virginia (.7% of the US), and 26% of the UK. Further, they have very little long-distance transmission (having built up their system around local plants), and transmission capacity is so limited that some new wind plants can't even be connected. I suspect that this reflects Germany's pre-E.U and pre-unification history. In any case, they'd have a lot more flexibility with more transmission capacity and interconnections with other countries, and could reduce generation and demand variance substantially.

My prediction for 2007 and the future is that we will power the 21st Century using the everlasting wind. I have a patent pending machine I will soon be testing in a wind tunnel. There is nothing the world needs more then unlimited energy. Think how the world will change once the new reality sinks in. Current technology keeps increasing the rotor diameter. Power is proportional to the square of the diameter (P = ½ ρ v3 A), but look at the advantage of the cube of the wind speed could provide.